Re: Setting up fixed point problem
- To: mathgroup at smc.vnet.net
- Subject: [mg42845] Re: Setting up fixed point problem
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 30 Jul 2003 19:30:44 -0400 (EDT)
- Organization: The University of Western Australia
- References: <bg800k$hk3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bg800k$hk3$1 at smc.vnet.net>, "Mark S. Coleman" <mark at markscoleman.com> wrote: > I'm working on a problem involving estimating the parameters of a fairly > complex probability distribution. Denote the vector of parameters by x. It > has been shown that the following "fixed point" equation provides a solution > > f(x(i+1)) = f(Sum[x(i)]} + v > > where v is a fixed vector of size conformable with x, and where i denotes > the fixed point iteration (i=0,1,2,...). > > In this case the function f is the digamma function, denoted PolyGamma[] in > Mathematica. I have two questions. First, can this be set-up using the > built-in > FixedPoint[] function, and second, can the digamma function be inverted in > a straightforward way to yield the value of x at iteration i ? See http://physics.uwa.edu.au/pub/Mathematica/PsiAsymptotics.nb Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul